This thesis presents a method for designing a flapping wing stroke for a flapping wing vehicle. A flapping wing vehicle is a vehicle such as a bird or an insect that uses its wings for propulsion instead of a conventional propeller or a jet engine. The intent of this research is to design a wing stroke that the wings can follow which will maintain the vehicle at a desired longitudinal flight path angle and velocity. The cost function is primarily a function of the flight path angle error, velocity error and control rate. The objective maneuver is to achieve a flight condition similar to the trim of a conventional fixed wing aircraft. Gliding configurations of the vehicle are analyzed to better understand flight in minimal energy configurations as well as the modes of the vehicle. A control law is also designed using Lyapunov’s direct method that achieves stable tracking of the wing stroke. Results are presented that demonstrate the ability of the method to design wing strokes that can maintain the vehicle at various flight path angles and velocities. The results of this research show that an optimal control problem can be posed such that the solution of the problem results in a wing stroke that a flapping wing vehicle can use to achieve a desired maneuver. The vehicle velocity is shown to be stable in controlled gliding flight and flapping flight.

In this thesis we study a new type of pursuit-evasion game, which we call the herding problem. Unlike typical pursuit evasion games where the pursuer aims to catch or intercept the evader, the goal of the pursuer in this game is to drive the evader to a certain location or region in the x-y plane. This herding model is proposed and represented using dynamic equations. The model is implemented in an effort to understand how two pursuers work cooperatively to drive multiple evaders to the desired destination following weighted time-optimal and effort-optimal control paths. Simulation of this herding problem is accomplished through dynamic programming by utilizing the SNOPT software in the MATLAB environment. The numerical solution gives us the optimal path for all agents and the corresponding controls as well as the relative distance and angle variables. The results show that the pursuers can work cooperatively to drive multiple evaders to the goal.

The optimal estimates of the eigenvalue gaps and eigenvalue ratios for the Sturm-Liouville operators have been of fundamental importance. Recently a series of works by Keller [7],Chern-Shen [3], Lavine [8], Huang [4] and Horvath [6] show that the first eigenvalue gap of the Schrodinger operator under Dirichlet boundary condition and the first eigenvalue ratio¡]£f2/£f1¡^of the string equation under Dirichlet boundary condition are dual problems of each other. Furthermore the problems when the potential functions and density functions are restricted to certain classes of functions can all be solved by a variational calculus method (differentiating the whole equation with respect to a parameter t to find £fn'(t)) together with some elementary analysis. In this thesis, we shall give a short survey of these result. In particular, we shall prove $3$ pairs of theorems. First when q is convex (£l is concave), then £f2-£f1¡Ù3 ¡]£f2/£f1¡Ù4¡^.If q is a single well and its transition point is £k/2 (£l is a single barrier and its transition point is £k/2), then £f2-£f1¡Ù3¡]£f2/£f1¡Ù4¡^.All these lower bounds are optimal when q(£l) is constant. Finally when q is bounded (£l is bounded), then £f2-£f1 is minimized by a step function (£f2/£f1 is minimized by a step function), after some additional conditions. We shell give a unified treatment to the above results.

The Mass Rapid Transit (MRT) systems have been built in many metropolitans to solve the public transportation problem such as traffic congestion. With such high investment cost, it is important to design a proper operation strategy to reduce the operational cost which achieving the system performance. With less ridership as compared to Taipei MRT system, the minimization of social cost which consists of energy consumption and the traveling time to complete the journey, has been investigated for Kaohsiung MRT (KMRT) system. By this way, the optimal coasting speed between train stations is solved according to the ridership and distance between the stations. The artificial neural network (ANN) has proposed in this thesis to determine the optimal coasting speed of the train set. The energy consumption and the traveling time to complete the journey between stations with various riderships are calculated by exactly the train performance simulation to generate the training data set. The objective function is defined by considering the energy consumption and the traveling time cost of passengers. By performing the ANN training, the ANN model is therefore obtained, which can be used to solve the optimal coasting speed of train sets. To demonstrate the effectiveness of the proposed ANN model, the forecasting of annual ridership for both Orange Line and Red Line of KMRT system is used. The optimal coasting speed and the corresponding profile of power consumption have been solved to minimize the social cost of MRT systems operation.

This thesis presents and develops efficient and effective methodologies for optimal hydraulic fracture design and fracture performance evaluation. These methods incorporate algorithms that simultaneously optimize all of the treatment parameters while accounting for required constraints. Damage effects, such as closure stress, gel damage and non-Darcy flow, are also considered in the optimal design and evaluation algorithms. Two user-friendly program modules, which are active server page (ASP) based, were developed to implement the utility of the methodologies. Case analysis was executed to demonstrate the workflow of the two modules. Finally, to validate the results from the two modules, results were compared to those from a 3D simulation program. The main contributions of this work are: An optimal fracture design methodology called unified fracture design (UFD) is presented and damage effects are considered in the optimal design calculation. As a by-product of UFD, a fracture evaluation methodology is proposed to conduct well stimulation performance evaluation. The approach is based on calculating and comparing the actual dimensionless productivity index of fractured wells with the benchmark which has been developed for optimized production. To implement the fracture design and evaluation methods, two web ASP based user interfaces were developed; one is called Frac Design (Screening), and the other is Frac Evaluation. Both modules are built to hold the following features. o Friendly web ASP based user interface o Minimum user input o Proppant type and mesh size selection o Damage effects consideration options o Convenient on-line help.

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Wind energy is the most abundant resource in the renewable energy portfolio. Increasing the wind capture capability improves the economic viability of this technology, and makes it more competitive with traditional fossil-fuel based supplies. Therefore, it is necessary to explore control strategies that maximize aerodynamic efficiency, thus, the wind energy capture. Several control algorithms are developed and compared during this research. A traditional feedback control is adapted as the benchmark approach, where the turbine torque and the blade pitch angle are used to control the wind turbine operation during partial and full load operations, correspondingly. Augmented feedback control algorithms are then developed to improve the wind energy harvesting. Optimal control methodologies are extensively explored to achieve maximal wind energy capture. Numerical optimization techniques, such as direct shooting optimization are employed. The direct shooting method convert the optimal control problem into a parameter optimization problem and use nonlinear programming algorithm to find the optimal solution. The dynamic programming, a global optimization approach over a time horizon, is also investigated. The dynamic programming finds the control inputs for the blade pitch angle and speed ratio to maximize the power coefficient, based on historical wind data. A dynamic wind turbine model has been developed to facilitate this process by characterizing the performance of the various possible input scenarios. Simulation results of each algorithm on real wind site data are presented to compare the wind energy capture under the proposed control algorithms with the traditional feedback control design. The result of the tradeoff analysis between the computation expense and the energy capture is also reported. / text

This thesis represents an attempt to generalize the classical Theory of Optimal Design to popular regression models, based on Rational and Spline approximations. The problem of finding optimal designs for such models can be reduced to solving certain minimax problems. Explicit solutions to such problems can be obtained only in a few selected models, such as polynomial regression. Even when an optimal design can be found, it has, from the point of view of modern nonparametric regression, certain drawbacks. For example, in the polynomial regression case, the optimal design crucially depends on the degree m of approximating polynomial. Hence, it can be used only when such degree is given/known in advance. We present a partial, but practical, solution to this problem. Namely, the so-called Super Chebyshev Design has been found, which does not depend on the degree m of the underlying polynomial regression in a large range of m, and at the same time is asymptotically more than 90% efficient. Similar results are obtained in the case of rational regression, even though the exact form of optimal design in this case remains unknown. Optimal Designs in the case of Spline Interpolation are also currently unknown. This problem, however, has a simple solution in the case of Cardinal Spline Interpolation. Until recently, this model has been practically unknown in modern nonparametric regression. We demonstrate the usefulness of Cardinal Kernel Spline Estimates in nonparametric regression, by proving their asymptotic optimality, in certain classes of smooth functions. In this way, we have found, for the first time, a theoretical justification of a well known empirical observation, by which cubic splines suffice, in most practical applications. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-07-18 16:06:06.767

This thesis proposes a new simulated annealing approach to solve multiple objective sequencing problems in mixed-model assembly lines. Mixed-model assembly lines are a type of production line where a variety of product models similar in product characteristics are assembled. Such an assembly line is increasingly accepted in industry to cope with the recently observed trend of diversification of customer demands. Sequencing problems are important for an efficient use of mixed-model assembly lines. There is a rich of criteria on which to judge sequences of product models in terms of line utilization. We consider three practically important objectives: the goal of minimizing the variation of the actual production from the desired production, which is minimizing usage variation, workload smoothing in order to reduce the chance of production delays and line stoppages and minimizing total set-ups cost. A considerate line manager would like to take into account all these factors. These are important for an efficient operation of mixed-model assembly lines. They work efficiently and find good solution in a very short time, even when the size of the problem is too large. The multiple objective sequencing problems is described and its mathematical formulation is provided. Simulated annealing algorithms are designed for near or optimal solutions and find an efficiency frontier of all efficient design configurations for the problem. This approach combines the SA methodology with a specific neighborhood search, which in the case of this study is a "swapping two sequence". Two annealing methods are proposed based on this approach, which differ only in cooling and freezing schedules. This research used correlation to describe the degree of relationship between results obtained by method B and other heuristics method and also for quality of our algorithm ANOVA's of output is constructed to analyse and evaluate the accuracy of the CPU time taken to determine near or optimal solution.

Long term asset creates more revenue, however it is riskier in a liquidity sense. Our question is: How does a liquidity constrained bank make decisions between profitability and liquidity? We present a computable DSGE model of banks optimal portfolio choices under liquidity constraints. Our theory predicts that liquidation plays an important role in a bank's portfolio model. Even though liquidation is an off-equilibrium phenomenon, banks can have rich loan portfolios due to the possibility of liquidation. Liquidity condition is a key factor in banks portfolio. In a moderate liquidity situation, a bank can lend more profitable longer term loans, however, if a shock in liquidity is expected, then the bank lends more loans in short term. According to the liquidity conditions, the bank can have medium term loans which are different from other previous literature. In addition, we extend our model to the bank's securities business where the bank's debts are largely short term deposit. Our theory predicts that the bank securities business produces a chasm between a real liquidity of economy and market liquidity. Banks can have more liquidity by selling their securitized loans, and as our model already pointed out, a good liquidity condition makes the bank have more profitable but less liquid long term loans. As a consequence, long term loans are accumulated with this securitization, simply because a long term loan gives higher revenue. Any market turbulence can invoke a problem in economy wide liquidity.